Franciscan University of Steubenville

Mathematics Science Classes

MTH 120

SURVEY OF MATHEMATICS is an introduction to various
topics in mathematics designed to teach critical thinking and to impart a
general knowledge and appreciation of mathematics. Topics will be
selected from logic, geometry, linear and exponential growth, personal
finance, discrete mathematics, probability, statistics, and social
choice theory. (Mathematics Core)3 credit hours

MTH 121

MATHEMATICS FOR EARLY AND MIDDLE GRADE TEACHERS I
includes such topics as an introduction to problem solving, set theory,
functions, logic, numeration systems, and other number bases, and an
overview of the real number system with its subsystems and related
properties. Historical development and mathematical connections are
stressed. The course is only for majors pursuing early childhood, middle
grades, or intervention specialist licensure. 3 credit hours

MTH 134

ELEMENTS OF GEOMETRY is designed for education
majors and focuses on properties of geometric figures, geometric
relations (congruence and similarity), measurement, estimation, plane
geometry, Euclidean and non-Euclidean geometries, coordinates and
transformations, and deductive arguments. The course will also include
historical highlights; teaching techniques and learning styles; and the
use of technology in instruction. Students will frequently engage in
group activities and peer teaching.Prerequisites: MTH 121 and 122, 155 3 credit hours

MTH 155

FINITE MATHEMATICS is an introduction to
mathematical topics and applications required by many college-level
major programs. The material covered includes equations, inequalities,
systems of linear equations and matrices, linear programming,
mathematics of finance, and probability.Prerequisite: 1 year of high school algebra3 credit hours

MTH 156

APPLIED CALCULUS is intended to follow MTH 155.
Topics include precalculus review, functions, limits differentiation and
application of the derivative, and integration and applications of the
integral.Prerequisite: 2 years of high school algebra> 3 credit hours

MTH 160

PRECALCULUS presents selected topics from algebra and elementary functions as preparation for studying calculus. (Communications Core)Prerequisite: Two years of high school mathematics including algebra and plane geometry3 credit hours

MTH 161

ANALYTIC GEOMETRY AND CALCULUS I studies
inequalities, relations, functions, graphs, straight lines, limits and
continuity, differentiation, and the definite integral. Students will
complete computer symbolic algebra (e.g. Maple) experiments. Historical
and career information is included.Prerequisite: Three years of high school mathematics including two years of algebra or MTH 160 4 credit hours

MTH 171

MATRIX THEORY I focuses on elementary matrix
algebra, which has become an integral part of the mathematical
background necessary for such diverse fields as electrical engineering,
education, chemistry and sociology, as well as for statistics, computer
science, and pure mathematics. Application is made to the solution of
linear systems.Corequisite: MTH 161 1 credit hour

MTH 172

MATRIX THEORY II continues with the applications of
matrix algebra to the solution of linear systems and to linear
transformations on abstract vector spaces. A special emphasis is placed
on applications to computer science.Prerequisite: MTH 171Corequisite: MTH 1621 credit hour

MTH 179

HISTORY OF MATHEMATICS provides an introduction to
the historical and philosophical development of mathematics, including
the contributions of underrepresented groups and diverse cultures. 1 credit hour

MTH 210

EUCLIDEAN AND NON-EUCLIDEAN GEOMETRY begins with a
close study of portions of Euclid’s Elements, including complete
coverage of the first book. The historical impact of his axiomatic
approach and its ultimate refinement in Hilbert’s axioms will be
explored. This course will cover some of the history of the attempts to
prove the Parallel Postulate, leading up to the discovery of
non-Euclidian geometries in the 19th century. The two main models of
non-Euclidean geometries (elliptic and hyperbolic) will be described and
some of their properties investigated. Finally, the history of geometry
since the discovery of non-Euclidean geometries (e.g. Kline’s Erlanger
Program) will be briefly covered. Prerequisites: One year of high school geometry or MTH 1343 credit hours

MTH 220

DISCRETE MATHEMATICS surveys proof techniques,
recursion, induction, modeling, and algorithmic thinking. Other topics
covered include set theory, discrete number systems, combinatorics,
graph theory, Boolean algebra, and a variety of applications. There is
an emphasis on oral and written communication of mathematical ideas,
cooperative learning, and the proofs of mathematical conjectures.Prerequisite: MTH 1613 credit hours

MTH 265

DIFFERENTIAL EQUATIONS presents ordinary
differential equations and their applications with an emphasis on
techniques of solution including numerical methods.Prerequisite: MTH 2613 credit hours

MTH 270

CHAOS AND FRACTALS examines the mathematics behind
two fascinating and inter-related topics, fractals and chaos. Chaos and
fractals are components of dynamics, a subject that studies how systems
change over time. Through computer experimentation and simulations,
students will experience how new mathematics is developed. Topics
covered include fractals: feedback and the iterator; classical fractals
and self-similarity; length, area, and dimension; fractals with a random
component; recursive structures including L-systems; attractors;
deterministic chaos; fixed points, stable and unstable; and the
period-doubling route to chaos. Prerequisites: MTH 162, 172 and at least 1 computer course3 credit hours

MTH 305

INTRODUCTION TO ABSTRACT ALGEBRA develops the
structural concepts that characterize abstract algebra. Topics in this
course will be selected from the following: elementary number theory,
groups, rings, integral domain, fields, and vector spaces. There is an
emphasis on the oral and written communication of mathematical ideas.
Students will frequently work in groups on special projects.Prerequisites: MTH 161-162, 2203 credit hours

MTH 311

LINEAR PROGRAMMING covers both the theory and
applications of linear programming, one of the leading methods for
large-scale optimization. The simplex method will be studied in detail.
Applications include product mix, diet, transportation, and network flow
problems. Integer programming will be touched on briefly. Computer
tools such as spreadsheet solvers will be introduced and used. Prerequisites: MTH 2203 credit hours

MTH 330

NUMBER THEORY AND CRYPTOGRAPHY covers the
fundamental algorithms used in both private key and public key
cryptography. Algorithms covered will include DES, AES, Diffie-Hellman,
and RSA. Traditional encryption methods such as Vigenere ciphers and
their cryptanalysis will be briefly described. The number theory needed
to understand primality testing and RSA encryption will be developed in
detail. Several programming projects aimed at implementing some of the
material will be given throughout the semester. Cross-listed with CSC 330 Prerequisites: CSC 141, 144, 171 or 280; and MTH 2203 credit hours

MTH 335

JUNIOR SEMINAR is designed to teach mathematical
science majors the skills necessary to learn mathematics on their own
and communicate their knowledge to others in oral and written form. All
students will attend presentations made by senior mathematics students.
Students will be required to write a short, independently-researched
paper and present it to the other students in the junior seminar. 1 credit hour

MTH 391

MTH 401

MATHEMATICAL STATISTICS I introduces a statistical
basis for decision making to the student of applied science in this
modern tool of analysis. This will be accomplished by studies in
probability theory for both discrete and continuous sample spaces and in
an introduction to statistical inference.Prerequisites: MTH 161-162 3 credit hours

MTH 402

MATHEMATICAL STATISTICS II is a continuation of MTH
401, covering additional concepts and techniques of statistics with an
emphasis on problem-solving approaches.Prerequisite: MTH 4013 credit hours

MTH 408

INTRODUCTION TO FUNCTIONS OF A COMPLEX VARIABLE
liberates the mathematician from the restrictions imposed by the domain
of real numbers when the broader field of complex numbers is made
available. Beginning with a study of complex numbers, this course
introduces the algebra and the calculus of elementary functions.Prerequisite: MTH 2613 credit hours

MTH 420

INTRODUCTION TO REAL ANALYSIS gives a theoretical
presentation of the real numbers, sequences, and their limits, including
lim sup and lim inf; continuity; sequences of functions and pointwise
and uniform convergence; and the (point set) topology of the reals.Prerequisites: MTH 220 and 261 3 credit hours

MTH 430

NUMERICAL ANALYSIS provides students with an
intuitive and working understanding of numerical methods of problem
solving, an appreciation of the concept of error and the need to control
it, and the ability to implement numerical methods using a computer.
Topics include: approximation of functions, interpolation, error
analysis, numerical integration and differentiation, numerical linear
algebra, and numerical solutions to differential equations.Prerequisites: MTH 161-162 and either CSC 141, 144, or 280 3 credit hours

MTH 434

SENIOR THESIS requires all mathematical science
students to write a thesis on an approved mathematical topic. Students
must consult closely with a departmental faculty member at each stage in
the development of their theses. The thesis will be presented to
students in the Junior Seminar.1 credit hour

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